We argue that the Kovtun--Son--Starinets (KSS) lower bound on the viscosity to entropy density ratio holds in fluid systems but is violated in solid materials with a non-zero shear elastic modulus. We construct explicit examples of this by applying the standard gauge/gravity duality methods to massive gravity and show that the KSS bound is clearly violated in black brane solutions whenever the massive gravity theories are of solid type. We argue that the physical reason for the bound violation relies on the viscoelastic nature of the mechanical response in these materials. We speculate on whether any real-world materials can violate the bound and discuss a possible generalization of the bound that involves the ratio of the shear elastic modulus to the pressure.
Relativistic fluid hydrodynamics, organized as an effective field theory in the velocity gradients, has zero radius of convergence due to the presence of non-hydrodynamic excitations. Likewise, the theory of elasticity of brittle solids, organized as an effective field theory in the strain gradients, has zero radius of convergence due to the process of the thermal nucleation of cracks. Viscoelastic materials share properties of both fluids and solids. We use holographic gauge theory/gravity correspondence to study all order hydrodynamics of relativistic viscoelastic media.
We introduce a kind of electromagnetism, which we call viscoelastic-electromagnetism, to investigate viscoelastic transport phenomena. It is shown that Cartan's formalism of general relativity is essential for viscoelastic theory, and then the corresponding electric and magnetic fields are regarded as a velocity gradient and a Burgers vector density, respectively. As an application of this formalism, the Streda formula for the Hall viscosity is obtained.
We study the ratio of the shear viscosity to the entropy density for various holographic superfluids. For the s-wave case, the ratio has the universal value 1/(4pi) as in various holographic models. For the p-wave case, there are two shear viscosity coefficients because of the anisotropic boundary spacetime, and one coefficient has the universal value. For the (p+ip)-wave case, the existing technique is not applicable since there is no tensor mode of metric perturbations which decouples from Yang-Mills perturbations. Our results indicate that the shear viscosity does not show a singular behavi…
Recently Eling and Oz [1] proposed a simple formula for the bulk viscosity of holographic plasma. They argued that the formula is valid in the high temperature (near-conformal) regime, but is expected to break down at low temperatures. We point out that the formula is in perfect agreement with the previous computations of the bulk viscosity of the cascading plasma [2,3], as well as with the previous computations of the bulk viscosity of N=2^* plasma [4,5]. In the latter case it correctly reproduces the critical behaviour of the bulk viscosity in the vicinity of the critical point with the vani…
A novel technique is used to compute the bulk viscosity of high temperature holographic gauge theory plasmas with softly broken conformal symmetry. Working in a black hole background which corresponds to a non-trivial solution to the Navier-Stokes equation, and using a Ward identity for the trace of the stress-energy tensor, it is possible to obtain an analytic expression for the bulk viscosity. This can be used to verify the high temperature limit of a conjectured bound on the bulk viscosity for these theories. The bound is saturated when the conformal symmetry-breaking operator becomes margi…
Motivated by gauge theory/string theory correspondence, a lower bound on the bulk viscosity of strongly coupled gauge theory plasma was proposed in arXiv:0708.3459. We consider strongly coupled N=4 supersymmetric Yang-Mills plasma compactified on a two-manifold of constant curvature beta. We show that the effective (1+1)-dimensional hydrodynamic description of the system is governed by the bulk viscosity violating the bound of arXiv:0708.3459, once beta<0.
Recently Eling and Oz (EO) proposed a formula for the holographic bulk viscosity, in arXiv:1103.1657, derived from the null horizon focusing equation. This formula seems different from that obtained earlier by Gubser, Pufu and Rocha (GPR) in arXiv:0806.0407 calculated from the IR limit of the two-point function of the trace of the stress tensor. The two were shown to agree only for some simple scaling cases. We point out that the two formulae agree in two non-trivial holographic theories describing RG flows. The first is the strongly coupled N=2* gauge theory plasma. The second is the semi-phe…
We show that the field theories dual to the homogeneous holographic models with spontaneously broken translations display several distinctive properties of quasicrystals, aperiodic crystals with long-range order (e.g. incommensurate charge density waves). This interpretation suggests that the longitudinal diffusive mode, observed in the spectrum of excitations of these systems, is the diffusive Goldstone boson typical of quasicrystals -- the phason. Moreover, following this idea, and using the effective field theory formalism for Goldstone modes in dissipative systems, we are able to derive th…
We show that the correct dual hydrodynamic description of homogeneous holographic models with spontaneously broken translations must include the so-called "strain pressure" -- a novel transport coefficient proposed recently. Taking this new ingredient into account, we investigate the near-equilibrium dynamics of a large class of holographic models and faithfully reproduce all the hydrodynamic modes present in the quasinormal mode spectrum. Moreover, while strain pressure is characteristic of equilibrium configurations which do not minimise the free energy, we argue and show that it also affect…
A holographic dual of a finite-temperature SU(N_c) gauge theory with a small number of flavours N_f << N_c typically contains D-branes in a black hole background. By considering the backreaction of the branes, we demonstrate that, to leading order in N_f/N_c, the viscosity to entropy ratio in these theories saturates the conjectured universal bound eta/s >= 1/4π. The contribution of the fundamental matter eta_fund is therefore enhanced at strong 't Hooft coupling lambda; for example, eta_fund ~ lambda N_c N_f T^3 in four dimensions. Other transport coefficients are analogously enhanced. These …
We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the dispersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in arXiv:0708.34…
Based on the gauge/gravity correspondence, the hydrodynamic response coefficients, shear and Hall viscosities, have been studied. The holographic model of Einstein-Maxwell- AdS $(3+1)$-dimensional system additionally coupled with the another gauge field mimicking the {\it dark matter} sector, as well as, gravitational Chern-Simons term bounded with a dynamical scalar field, were taken into account. Condensation of the scalar field provides the parity violating term. Both shear and Hall viscosities have been calculated and their dependence on $α$ - the coupling constant between matter and {\it …
We provide the first characterization of the nonlinear and time dependent rheologic response of viscoelastic bottom-up holographic models. More precisely, we perform oscillatory shear tests in holographic massive gravity theories with finite elastic response, focusing on the large amplitude oscillatory shear (LAOS) regime. The characterization of these systems is done using several techniques: (I) the Lissajous figures, (II) the Fourier analysis of the stress signal, (III) the Pipkin diagram and (IV) the dependence of the storage and loss moduli on the amplitude of the applied strain. We find …
We construct a slowly varying space-time dependent holographic superfluid and compute its transport coefficients. Our solution is presented as a series expansion in inverse powers of the charge of the order parameter. We find that the shear viscosity associated with the motion of the condensate vanishes. The diffusion coefficient of the superfluid is continuous across the phase transition while its third bulk viscosity is found to diverge at the critical temperature. As was previously shown, the ratio of the shear viscosity of the normal component to the entropy density is 1/(4 pi). As a conse…
We study the spontaneous parity breaking and generating of Hall viscosity and angular momentum in holographic p+ip model, which can describe strongly-coupled chiral superfluid states in many quantum systems. The dual gravity theory, an SU(2) gauge field minimally coupled to Einstein gravity, is parity-invariant but allows a black hole solution with vector hair corresponding to a parity-broken superfluid state. We show that this state possesses a non-vanishing parity-odd transport coefficient -- Hall viscosity -- and an angular momentum density. We first develop an analytic method to solve this…
We revisit the membrane paradigm calculations of the holographic shear viscosity tensor of strongly coupled isotropic plasmas with Einstein gravity dual by emphasizing the fact which was overlooked in the previous literatures that the shear viscosity is a fourth-rank tensor. Using the membrane paradigm we show that depending on whether the holographic shear viscosity tensor to entropy density ratio is η^j_i^j_i/s or η^{jiji}/s or η_{jiji}/s, we can derive three distinct formulae for the holographic shear viscosity tensor to entropy density ratios given explicitly in terms of the background met…
We develop analytic techniques to construct the leading dissipative terms in a derivative expansion of holographic fluids. Our basic ingredient is the Crnkovic-Witten symplectic current of classical gravity which we use to extract the dissipative transport coefficients of holographic fluids, assuming knowledge of the thermodynamics and the near horizon geometries of the bulk black hole geometries. We apply our techniques to non-conformal neutral fluids to reproduce previous results on the shear viscosity and generalise a known expression for the bulk viscosity.
In (2+1)-dimensional systems with broken parity, there exists yet another transport coefficient, appearing at the same order as the shear viscosity in the hydrodynamic derivative expansion. In condensed matter physics, it is referred to as "Hall viscosity". We consider a simple holographic realization of a (2+1)-dimensional isotropic fluid with broken spatial parity. Using techniques of fluid/gravity correspondence, we uncover that the holographic fluid possesses a nonzero Hall viscosity, whose value only depends on the near-horizon region of the background. We also write down a Kubo's formula…
We compute the bulk viscosity in holographic models dual to theories with Lifshitz scaling and/or hyperscaling violation, using a generalization of the bulk viscosity formula derived in arXiv:1103.1657 from the null focusing equation. We find that only a class of models with massive vector fields are truly Lifshitz scale invariant, and have a vanishing bulk viscosity. For other holographic models with scalars and/or massless vector fields we find a universal formula in terms of the dynamical exponent and the hyperscaling violation exponent.
We study holographic RG flow of the shear viscosity tensor of anisotropic, strongly coupled N=4 super-Yang-Mills plasma by using its type IIB supergravity dual in anisotropic bulk spacetime. We find that the shear viscosity tensor has three independent components in the anisotropic bulk spacetime away from the boundary, and one of the components has a non-trivial RG flow while the other two have a trivial one. For the component of the shear viscosity tensor with non-trivial RG flow, we derive its RG flow equation, and solve the equation analytically to second order in the anisotropy parameter …
In this paper we investigate the ratio of shear viscosity to entropy density, $η/s$, in hyperscaling violating geometry with lattice structure. We show that the scaling relation with hyperscaling violation gives a strong constraint to the mass of graviton and usually leads to a power law of temperature, $η/s\sim T^κ$. We find the exponent $κ$ can be greater than two such that the new bound for viscosity raised in arXiv:1601.02757 is violated. Our above observation is testified by constructing specific solutions with UV completion in various holographic models. Finally, we compare the boundedne…
We have modified the holographic model of Saremi and Son by using a charged black brane, instead of a neutral one, such that when the bulk pseudo scalar potential is made of quadratic and quartic terms, parity can still be broken spontaneously in the boundary theory. In our model, the 3+1 dimensional bulk has a pseudo scalar coupled to the gravitational Chern-Simons term in the anti de Sitter charged black brane back ground. Parity could be broken spontaneously in the bulk by the pseudo scalar hairy solution and give rise to non-zero Hall viscosity at the boundary theory.
We study the conductivity and shear viscosity tensors of a strongly coupled N=4 super-Yang-Mills plasma which is kept anisotropic by a theta parameter that depends linearly on one of the spatial dimensions. Its holographic dual is given by an anisotropic axion-dilaton-gravity background and has recently been proposed by Mateos and Trancanelli as a model for the pre-equilibrium stage of quark-gluon plasma in heavy-ion collisions. By applying the membrane paradigm which we also check by numerical evaluation of Kubo formula and lowest lying quasinormal modes, we find that the shear viscosity pure…
Kovtun, Son and Starinets proposed a bound on the shear viscosity of any fluid in terms of its entropy density. We argue that this bound is always saturated for gauge theories at large 't Hooft coupling, which admit holographically dual supergravity description.
We study a bottom-up holographic model of large-Nc Yang-Mills theory, in which conformal invariance is broken through the introduction of a dilaton potential on the gravity side. We use the model to calculate the spectral densities of the shear and bulk channels at finite temperature. In the shear channel, we compare our results to those derived in strongly coupled N=4 Super Yang-Mills theory as well as in weakly coupled ordinary Yang-Mills. In the bulk channel, where the conformal result is trivial, we make comparisons with both perturbative and lattice QCD. In both channels, we pay particula…
We use the holographic approach to compare the Hall viscosity $η_H$ and the angular momentum density ${\cal J}$ in gapless systems in $2+1$ dimensions at finite temperature. We start with a conformal fixed point and turn on a perturbation which breaks the parity and time reversal symmetries via gauge and gravitational Chern-Simons couplings in the bulk. While the ratio of $η_H$ and ${\cal J}$ shows some universal properties when the perturbation is slightly relevant, we find that the two quantities behave differently in general. In particular, $η_H$ depends only on infrared physics, while ${\c…
We study odd viscosity in a holographic model of a Weyl semimetal. The model is characterised by a quantum phase transition from a topological semimetal to a trivial semimetal state. Since the model is axisymmetric in three spatial dimensions there are two independent odd viscosities. Both odd viscosity coefficients are non-vanishing in the quantum critical region and non-zero only due to the mixed axial gravitational anomaly. It is therefore a novel example in which the mixed axial gravitational anomaly gives rise to a transport coefficient at first order in derivatives at finite temperature.…
A computation of the quotient of shear viscosity to entropy density, or KSS number $η/s$ is performed, in the non-relativistic and classical regime, first in Chiral Perturbation Theory, and then in the $SO(g+1)/SO(g)$ Non-Linear Sigma Model in the large $g$ limit. Both are field theories stemming from a renormalizable Sigma Model but in spite of that, we explicitly calculate how one undercomes the KSS bound by increasing the number of degenerate pions sufficiently. However we argue that particle production could still keep the validity of the KSS bound in the weak sense. We also show how a lar…
We consider a holographic model of chiral superfluidity whose bulk is Einstein Yang-Mills and compute viscosity and conductivity responses away from the probe limit. We calculate Hall viscosity and analyze its relationship to the superfluid density and the shift. We find that the relationship between these quantities derived from effective field theory at zero temperature persists for all temperatures: for $p\pm ip$ their ratio is equal to $\mp1/2$. At low temperatures the system develops a Lifshitz throat, indicating an anisotropic scaling symmetry in the infrared dynamics.
Based on AdS/CFT correspondence, we build a deep neural network to learn black hole metrics from the complex frequency-dependent shear viscosity. The network architecture provides a discretized representation of the holographic renormalization group flow of the shear viscosity and can be applied to a large class of strongly coupled field theories. Given the existence of the horizon and guided by the smoothness of spacetime, we show that Schwarzschild and Reissner-Nordström metrics can be learned accurately. Moreover, we illustrate that the generalization ability of the deep neural network can …
We calculate the bulk viscosity, drag force and jet quenching parameter in Improved Holographic QCD. We find that the bulk viscosity rises near the phase transition but does not exceed the shear viscosity. The drag force shows the effects of asymptotic freedom both as a function of velocity and temperature. It indicates diffusion times of heavy quarks in rough agreement with data. The jet quenching parameter values computed via the light-like Wilson loop are in the lower range suggested by data.
We present a strange metal, described by a holographic duality, which reproduces the famous linear resistivity of the normal state of the copper oxides, in addition to the linear specific heat. This holographic metal reveals a simple and general mechanism for producing such a resistivity, which requires only quenched disorder and a strongly interacting, locally quantum critical state. The key is the minimal viscosity of the latter: unlike in a Fermi-liquid, the viscosity is very small and therefore is important for the electrical transport. This mechanism produces a resistivity proportional to…
Gauss-Bonnet holographic fluid is a useful theoretical laboratory to study the effects of curvature-squared terms in the dual gravity action on transport coefficients, quasinormal spectra and the analytic structure of thermal correlators at strong coupling. To understand the behavior and possible pathologies of the Gauss-Bonnet fluid in $3+1$ dimensions, we compute (analytically and non-perturbatively in the Gauss-Bonnet coupling) its second-order transport coefficients, the retarded two- and three-point correlation functions of the energy-momentum tensor in the hydrodynamic regime as well as …
The viscosity of the Quark-Gluon Plasma (QGP) is usually described holographically by the entropy-normalized dynamic viscosity $η/s$. However, other measures of viscosity, such as the kinematic viscosity $ν$ and the Reynolds number $Re$, are often useful, and they too should be investigated from a holographic point of view. We show that a simple model of this kind puts an upper bound on $Re$ for nearly central collisions at a given temperature; this upper bound is in very good agreement with the observational lower bound (from the RHIC facility). Furthermore, in a holographic approach using on…
Inspired by recent experiments on graphene, we examine the non-dissipative viscoelastic response of anisotropic two-dimensional quantum systems. We pay particular attention to electron fluids with point group symmetries, and those with discrete translational symmetry. We start by extending the Kubo formalism for viscosity to systems with internal degrees of freedom and discrete translational symmetry, highlighting the importance of properly considering the role of internal angular momentum. We analyze the Hall components of the viscoelastic response tensor in systems with discrete point group …
We show how a Hall viscosity induced by a magnetic field can be generated in strongly coupled theories with a holographic dual. This is achieved by considering parity-breaking higher derivative terms in the gravity dual. These terms couple the Riemann curvature tensor to the field strength of a gauge field dual to the charge current, and have an analog in the field theory side as a coupling between the "Euler current" and the electromagnetic field. As a concrete example, we study the effect of the new terms in the thermodynamic and transport properties of a strongly coupled magnetized plasma d…
We numerically simulate gravitational shock wave collisions in a holographic model dual to a non-conformal four-dimensional gauge theory. We find two novel effects associated to the non-zero bulk viscosity of the resulting plasma. First, the hydrodynamization time increases. Second, if the bulk viscosity is large enough then the plasma becomes well described by hydrodynamics before the energy density and the average pressure begin to obey the equilibrium equation of state. We discuss implications for the quark-gluon plasma created in heavy ion collision experiments.
A finite temperature extension of the effective holographic models for QCD (EHQCD), proposed in Ref.[1], is investigated in the present work. EHQCD models are characterized by two parameters, the conformal dimension of the relevant operator that deforms the CFT and the associated coupling. We find that black hole solutions appear at temperatures higher than some temperature $T_{min}$ and can be categorized in two classes: large and small black holes. A large black hole is thermally stable and it is therefore interpreted as the gravity dual of a non-conformal plasma. A small black hole, on the …
We show that, in a holographic or gauge-gravity approach to the study of the Quark-Gluon Plasma, the specific entropy density of the plasma produced in a peripheral heavy-ion collision can be strongly suppressed relative to its value for central collisions at the same impact energy; this is connected with the strong vorticity fields which are now known to characterize the peripheral case. This implies, within the holographic model, that the shear viscosity of `peripheral plasmas' may be considerably lower than that of the corresponding `central plasmas', with potentially important consequences…
We study the mechanical response under time-dependent sources of a simple class of holographic models that exhibit viscoelastic features. The ratio of viscosity over elastic modulus defines an intrinsic relaxation time scale -- the so-called Maxwell relaxation time $τ_M$, which has been identified traditionally with the relaxation time scale. We compute explicitly the relaxation time in our examples and that it differs from $τ_M$. At high temperatures $τ_M$ over-estimates the actual relaxation time, although not by much and moreover it still captures reasonably well the temperature behaviour. …
